Particle Image Velocimetry Technique Research Articles

Wind Tunnel Experiments on Parallel Blade–Vortex Interaction with Static and Oscillating Airfoil

This study aims to experimentally investigate the effects of parallel blade–vortex interaction (BVI) on the aerodynamic performances of an airfoil, in particular as a possible cause of blade stall, since similar effects have been observed in literature in the case of perpendicular BVI. A wind tunnel test campaign was conducted reproducing parallel BVI on a NACA 23012 blade model at a Reynolds number of 300,000. The vortex was generated by impulsively pitching a second airfoil model, placed upstream. Measurements of the aerodynamic loads acting on the blade were performed by means of unsteady Kulite pressure transducers, while particle image velocimetry (PIV) techniques were employed to study the flow field over the blade model. After a first phase of vortex characterisation, different test cases were investigated with the blade model both kept fixed at different incidences and oscillating sinusoidally in pitch, with the latter case, a novelty in available research on parallel BVI, representing the pitching motion of a helicopter main rotor blade. The results show that parallel BVI produces a thickening of the boundary layer and can induce local flow separation at incidences close to the stall condition of the airfoil. The aerodynamic loads, both lift and drag, suffer important impulsive variations, in agreement with literature on BVI, the effects of which are extended in time. In the case of the oscillating airfoil, BVI introduces hysteresis cycles in the loads, which are generally reduced. In conclusion, parallel BVI can have a detrimental impact on the aerodynamic performances of the blade and even cause flow separation, which, while not being as catastrophic as in the case of dynamic stall, has relatively long-lasting effects.

Experimental dataset investigation of deep recurrent optical flow learning for particle image velocimetry: flow past a circular cylinder

Current optical flow-based neural networks for particle image velocimetry (PIV) are largely trained on synthetic datasets emulating real-world scenarios. While synthetic datasets provide greater control and variation than what can be achieved using experimental datasets for supervised learning, it requires a deeper understanding of how or what factors dictate the learning behaviors of deep neural networks for PIV. In this study, we investigate the performance of the recurrent all-pairs field transforms-PIV (RAFTs-PIV) network, the current state-of-the-art deep learning architecture for PIV, by testing it on unseen experimentally generated datasets. The results from RAFT-PIV are compared with a conventional cross-correlation-based method, Adaptive PIV. The experimental PIV datasets were generated for a typical scenario of flow past a circular cylinder in a rectangular channel. These test datasets encompassed variations in particle diameters, particle seeding densities, and flow speeds, all falling within the parameter range used for training RAFT-PIV. We also explore how different image pre-processing techniques can impact and potentially enhance the performance of RAFT-PIV on real-world datasets. Thorough testing with real-world experimental PIV datasets reveals the resilience of the optical flow-based method’s variations to PIV hyperparameters, in contrast to the conventional PIV technique. The ensemble-averaged root mean squared errors between the RAFT-PIV and Adaptive PIV estimations generally range between 0.5–2 (px) and show a slight reduction as particle densities increase or Reynolds numbers decrease. Furthermore, findings indicate that employing image pre-processing techniques to enhance input particle image quality does not improve RAFT-PIV predictions; instead, it incurs higher computational costs and impacts estimations of small-scale structures.

Experimental study on vertical seepage of coarse-grained calcareous sand

Calcareous sand, a special geotechnical material employed as foundation fill in numerous reef constructions, exhibits susceptibility to seepage deformation in complex marine dynamic environments. Its permeability characteristics are notably distinct from conventional terrestrial soil, making the understanding of these properties critical for further applications. This study conducted vertical seepage tests on coarse-grained calcareous sand samples with varying coefficients of uniformity (Cu), coefficients of curvature (Cc), relative compactions (Dr), and soil skeletal structures. These tests utilized a custom-designed apparatus, supplemented with image binarization and particle image velocimetry techniques. Based on the results, the findings revealed a three-stage vertical seepage process: steady seepage, hydraulic adjustment, and seepage failure. The permeability coefficient k20 of the calcareous sand samples was observed to transition from a decreasing to an increasing trend with rising Cu and Cc values. Moreover, the k20 of tightly compacted and medium-tightly compacted samples exceeded that during the steady seepage stage upon entering the second stage, while the opposite holds true for relatively loose samples. The spatial organization of the sample skeleton had a considerable impact on its permeability, with coarse-grained calcareous sand imposing a greater constraint on fine particle migration compared to river sand.

Large-scale flow field super-resolution via local-global fusion convolutional neural networks

Particle image velocimetry (PIV) techniques have a limited field of view of the flow field and can only capture high-resolution flow fields in localized areas. To obtain a larger measurement range, multiple cameras must be used to capture the flow field simultaneously and then stitch the parts together. However, this method can be expensive. We propose the local-global fusion convolutional neural network (LGF-CNN) for reconstructing large-field flow fields with high spatial resolution based only on two flow data types: local small-field high spatial resolution wake velocity fields and global large-field low spatial resolution velocity fields. The core of the model consists of convolutional neural network (CNN) architecture to learn the mapping relationship between the small field of view with high spatial resolution and the large field of view with low spatial resolution. Using the effectively trained LGF-CNN model, we demonstrate its ability to reconstruct high-resolution velocity fields around the circular cylinder. The LGF-CNN is rigorously validated on a number of representative datasets, including simulated data for Reynolds numbers of 200 and 500, as well as experimental data for a Reynolds number of 3.3 × 104 with the steady jet at the rear stagnation point of the cylinder. The results demonstrate the ability of LGF-CNN to generate accurate velocity fields with high spatial resolution, including reliable detection of high-frequency components. The proposed method could reduce the number of cameras required for large-field, high spatial resolution PIV measurements, thereby reducing experimental costs.

Interfacial Effects of Nanostructured Doubly Reentrant Surfaces on the Evolution of Local Concentration and Fluid Flow in an Evaporating Droplet.

Surface modification, such as bioinspired nanostructured doubly reentrant surfaces that have presented superhydrophobic wettability even under low-surface-tension liquid, is a very promising technology for controlling droplet dynamics, heat transfer, and evaporation. In this article, we investigate the interfacial effects of nanostructured doubly reentrant surfaces on the flow behaviors and local concentration evolution during the evaporation of an ethanol/water multicomponent droplet. Using particle image velocimetry (PIV) and novel aggregate-induced emission-based (AIE) techniques, the flow patterns and local concentration distributions on both hydrophobic and nanostructured doubly reentrant surfaces were probed and compared. It is found that in addition to the established Marangoni flow-dominated stage, transition stage, and buoyancy-induced flow-dominated stage, a new transition stage and a rolling stage for the nanostructured doubly reentrant surface are detected in the late evaporation period. Differences in the local concentration distribution evolution occur depending on the hydrophobicity of the surface on which the droplet is placed. For the hydrophobic surface, a nonuniform local concentration distribution exists consistently, with a high water fraction in a shell-shaped region near the liquid-air interface and a secondary concentration gradient within this shell-shaped region. The concentration distribution on the nanostructured doubly reentrant surface evolves in a more complex manner, with a strip-shaped region of high water fraction forming in the intermediate stage and then reorganized by rolling flow in the late stage. Finally, theoretical analysis combining PIV and AIE visualization results reveals that the variations in droplet concentration distributions on surfaces with different hydrophobicities exert a significant impact on evaporative behaviors. These behaviors, in turn, affect the evolution of the local concentration distribution.

Insights into turbulent flow structure and energy dissipation in centrifugal pumps: A study utilizing time-resolved particle image velocimetry and proper orthogonal decomposition

The purpose of the study is to investigate the flow structure and energy dissipation mechanism within centrifugal pump impellers. The velocity fields at the mid-sections of the flow passages of 4- and 5-blade impellers were measured under various flow rates using the Time-resolved Particle Image Velocimetry (TR-PIV) technique; the proper orthogonal decomposition (POD) analysis was performed to extract flow structures with different scales; the dissipation rate was estimated using the large-eddy PIV method; the correlation between turbulent kinetic energy (TKE) and dissipation rate was measured using the cross-correlation analysis. The findings are as follows: impeller with more uniform and stable flow, the scale and energy contribution of large-scale structures in lower order modes are smaller, leading to higher impeller efficiency; large-scale structures identified in the low-order modes correspond to locations of high TKE and dissipation areas; the high velocity gradients within the impeller passage and the interactions between large-scale flow structures encourage the breakup of large-scale turbulent structures into dissipative-scale structures; the correlation between TKE and dissipation rate reflects the extent to which large-scale flow structures within the impeller passage break up into dissipative scales.

Investigation of fluid flow during flow boiling inside a horizontal rectangular channel with single-sided heating using particle image velocimetry

Subcooled flow boiling is a highly efficient cooling systems for thermal management systems. This study explores the intricate dynamics of subcooled flow boiling within a horizontal channel, investigating the impact of vapor generation on liquid-phase velocity using Particle Image Velocimetry (PIV) and advanced image processing techniques. Four mass flow rates ranging from 5–20 g/s with subcooled inlet conditions are investigated in a rectangular channel with single-sided heating. Three regions of interest along the heated channel are investigated for instantaneous PIV analysis. The PIV system captures detailed velocity profiles, illustrating the impact of varying mass flow rates and heat flux levels on flow behavior. Vapor masking techniques are introduced to enhance the precision of PIV data by mitigating interference from the vapor phase. Results demonstrate the influence of vapor bubbles on flow resistance, revealing non-uniform velocity distributions and turbulence near the liquid–vapor interface. The study emphasizes the critical role of inertia and buoyancy forces in shaping the velocity profiles. Moreover, the investigation sheds light on the effects of flow rates on the interfacial behaviors, hinting at a transition point between 10 and 15 g/s. In summary, this research contributes valuable insights into the nuanced dynamics of flow boiling, laying the foundation for future studies on turbulence, heat transfer, and phase-change phenomena in two-phase thermal management systems.

Effects of interface friction states on plastic deformation in metal surface and bulk

Interface friction at the tool/die-material interface plays a pivotal role in metal plastic processes, significantly impacting material deformation behavior near the contact surface. This study focuses on understanding friction-induced deformation, particularly the plastic boundary layer and surface expansion behavior, at the tool/die-material interface by employing direct in-situ observations, coupled with high-speed imaging and particle image velocimetry techniques. It proves that interface friction determines the wall-slip behaviors and subsequently results in the non-uniform surface expansion distribution. Moreover, our results indicate that the application of lubricant alters the wall-slip velocity and localized surface expansion by 60% and 76%, respectively, at the contact interface. Based on these observations, a quantitative method for assessing the effectiveness of lubrication is proposed.

Numerical Analysis of Convective Heat Transfer in Quenching Treatments of Boron Steel under Different Configurations of Immersed Water Jets and Its Effects on Microstructure

In this work, the effects of jet impact angle and water flow on the heat-transfer coefficient in boron steel probes were analyzed. Angles of 90°, 75° and 60° were used with stirring flows of 33 l·min−1, 25 l·min−1, 13 l·min−1 and 6 l·min−1. The aim consisted of determining the heat-extraction rates by analyzing the correlation programmed in the Ansys Fluent 2020R2 software when different cooling conditions are used, avoiding many experiments, and establishing quenching conditions free of surface defects on the workpiece. This process is currently used in heavy machinery, requiring high hardness and wear resistance. The fluid-dynamic field was validated using a scale physical model using the particle image velocimetry technique, PIV. In contrast, the thermal field was validated with transient state experiments solving the inverse heat conduction problem, IHCP. The results show that for high flows (33 l·min−1), the jets with an angle of 90° impact the entire surface of the piece, but their cooling rate is slower compared to the other angles, being 243.61 K·s−1, and 271.70 K·s−1, 329.56 K·s−1 for 75° and 60°, respectively. However, for low flows (6 l·min−1), the impact velocities are very similar for the three cases, promoting more homogeneous cooling rates of 58.47 K·s−1, 73.58 K·s−1 and 63.98 K s−1 for angles of 90°, 75° and 60°, respectively. Likewise, through the use of CCT diagrams, it was determined that regardless of the cooling rate, the final structure will always be a mixture of martensite–bainite due to the effect of boron as determined experimentally, which implies a more significant proportion of martensite at higher cooling rates.

Centrifuge model tests on an anchor pile under cyclic oblique pullout load using transparent sand

Cyclic load on anchor piles of single point mooring systems is an important issue, and the cyclic behavior of anchor piles has a connection with the surrounding soil displacement. Based on transparent sand and particle image velocimetry (PIV) technique, centrifuge model tests on the pile subjected to oblique pullout load were conducted. The cyclic pile performance and the soil displacement field under various cyclic load characteristics were studied. The mechanism for the cyclic response of anchor piles was investigated. It can be observed by transparent sand that the failure mode of the pile is a combination of vertical and lateral translation without rotation. The post-cyclic pullout bearing capacities are decreased with the increasing of the cyclic amplitude and number of cycles, but the pile vertical displacement and the soil displacement are increased at the same post-cyclic reload. During the cyclic load period, the pile produces cumulative displacement due to soil particle movement, especially vertical displacement that can reduce embedment depth and bearing capacity. However, the shakedown behaviors of the cumulative displacement and post-cyclic bearing capacity of the pile occur, because the increasing rate of the soil displacement is decreased with loading cycles.

High-speed photography and particle image velocimetry of cavitation in a Venturi tube

This article details the construction of an experimental visualization platform for observing cavitation. The platform uses high-speed photography and particle image velocimetry (PIV) techniques to conduct experimental research into the flow pattern and vortex field of cavitation in Venturi tubes. Dynamic mode decomposition is employed to extract the energy distribution characteristics of the cavitation flow field. Cavitation occurs at an exit-to-inlet pressure ratio of 0.595, and the length of the cavitation zone increases as this ratio decreases. When the pressure ratio reaches 0.280, the flow rate remains almost constant and the flow becomes chocked. The cavitation shape evolves periodically in the chocking flow, and the cavitation zone can be divided into three parts: an initiation and development area, a fusion area, and a collapse area. The fusion area exhibits periodic changes in the form of contraction, expansion, and re-contraction. Near the wall, the collapse area exhibits complex boundary conditions, with re-entrant jet causing bubble aggregation, rolling, and shedding. PIV and energy extraction reveal that vortices primarily appear near the wall, where they undergo a periodic process of fragmentation and fusion. The strength of the vortices exhibits a small–large–small pattern that is related to the cloud aggregation, rolling, and shedding caused by the re-entrant jet.

FLUJO PULSÁTIL DE FLUIDOS VISCOELÁSTICOS EN TUBOS

In this study, we present an experimental investigation of the flow structure changes in non-Newtonian fluids subjected to periodic variable fluxes inside rigid-walled tubes. We employ a liquid mixture composed of water and polyacrylamide to account for various rheological properties. We obtain the velocity fields for each experimental case using the Particle Image Velocimetry (PIV) technique and we analyse their variations based on different properties of the pulsatile input signal. Reynolds numbers between 200 and 350 are considered, with a 10% variation in amplitude.

Experimentally Closing the Balance of Progress of Reaction in Premixed Turbulent Combustion in the Thin Flame Regime

We investigate the possibility of determining the local turbulent flame speed by measuring the individual terms in the balance of a mean progress of reaction variable for the case of a low turbulence methane-air Bunsen flame in the thin flame regime. Velocity distributions and flame edge positions were measured by particle image velocimetry techniques at 3 kHz for a flame stabilized by a surrounding pilot of the same stoichiometry, for a turbulent Reynolds number around 66 and Karlovitz numbers of the order of 4. The conservation equation for mean progress variable was analyzed along different streamlines as a balance of terms expressed as velocities, including terms for convection, turbulent diffusion, mean reaction, and turbulent and molecular diffusion. Each term was estimated from local velocities and flame locations using a thin flame approximation, and their uncertainty was evaluated based on propagation of experimentally measured statistical correlations. The largest terms were the convective and reaction terms, as expected, with smaller roles for turbulent and molecular diffusion across the flame brush. Countergradient diffusion and transition to gradient diffusion were observed across the flame brush. Closure of the balance of terms in the conservation equations using independently measured terms was not consistently achieved across the flame brush within the reckoned uncertainties, arriving at a balance within 20–30% of the absolute value. Testable hypotheses are offered for the possible reasons for the mismatch, including the role of spatial filtering and 3D effects on the reaction rate term. Finally, the experiments identify the inaccuracies in measuring a true local turbulent flame speed, and suggest a consistent methodology to reduce errors in such estimations. This is the first time such a detailed experimental closure is attempted for any configuration. The results suggest that the significant improvements in spatial resolution are necessary for a full closure.

On the behaviour of impinging sweeping jets: effects of the mixing chamber length, the feedback channel minimum cross-sectional area and the nozzle-to-plate distance

An experimental investigation on the effects of the mixing chamber length, the feedback channel minimum cross-sectional area and the nozzle-to-plate distance on the external flow field of impinging sweeping jets is performed by employing the Particle Image Velocimetry (PIV) technique. Three sweeping jet devices, characterized by different mixing chamber lengths (Lf/w=4.5,3.5,2.5, being w the width of the exit nozzle throat section), are investigated. Furthermore, in order to analyse different minimum cross-sectional area values, the geometry of the feedback channels of the device characterized by the longest mixing chamber length is varied. In particular, five different values of g/w (1, 0.67, 0.50, 0.33, and 0.17) are taken into account, being g the minimum passage width of the feedback channels. Time-averaged and phase-averaged measurements are carried out for non-dimensional nozzle-to-plate distances H/w ranging between 2 and 10, with a spacing of 2. As for the effects of the mixing chamber length, the devices characterized by Lf/w<4.5 do not generate an oscillating jet, thus the time-averaged flow field exhibits a single jet structure, while a twin-jet pattern is found for the device having Lf/w=4.5, due to the oscillating motion of the jet. Furthermore, due to the absence of the jet oscillation, the values assumed by the phase-correlated kinetic energy (PKE) are significantly lower for the devices having Lf/w<4.5. Moreover, for the latter devices, the highest values of the turbulent kinetic energy (TKE) are reached in the jet shear layers, which are aligned to the streamwise direction, instead, for the device having Lf/w=4.5, the TKE assumes higher values in proximity of the jet centreline. As for the effects of the feedback channel minimum cross-sectional area, the decrease of g/w determines an increase of the oscillation frequency and a reduction of the jet oscillation amplitude, with a subsequent strong decrease of the PKE and an increase of the TKE values in proximity of the jet centreline. As regards the effects of the nozzle-to-plate distance, by increasing this parameter for the device having Lf/w=4.5 the jet no longer sweeps in a rigid-like way between the two most deflected positions in the external flow field and the PKE values in the stagnation regions decrease.

Tip effects on three-dimensional flow structures over low-aspect-ratio plates: mechanisms of spanwise fluid transport

Three-dimensional flows over low-aspect-ratio rectangular flat plates ( ${A{\kern-4pt}R} = 1.00$ – $1.50$ ) are investigated using tomographic and planar particle image velocimetry techniques. The chord-based Reynolds number is $5400$ , and the angle of attack is fixed at $6^\circ$ . This study reveals for the first time the interplay between spanwise fluid transport and downwash, both originating from the tip effects. Spanwise fluid transport promotes the formation and subsequent coherent development of leading-edge vortices, whereas downwash stabilizes the flow. Specifically, two mechanisms related to spanwise fluid transport are revealed. First, the spanwise fluid transport enhances the intensity of the reversed flow, promoting the shear layer roll-up and vortex shedding. Second, the near-wall spanwise flow interacts with the shed C-shape vortices, thereby strengthening the vortex heads. In particular, through these interactions, spanwise fluid transport can sustain the coherence of the C-shape vortices until the vortex heads split in a regular fashion. Consequently, the C-shape vortices are transformed into novel Þ-shape vortices for the plates of ${A{\kern-4pt}R} \leq 1.25$ , which supplements the previously discovered transformation from C-shape to M-shape vortices for larger ${A{\kern-4pt}R}$ plates. Downstream of this novel vortex-splitting transformation, two fundamental processes contribute to the formation of hairpin vortices. The above comprehensive understanding of complete vortex evolution routine provides valuable insights into the tip effects on the formation of three-dimensional flows over low- ${A{\kern-4pt}R}$ plates.

Reinforcement treatment of dredging sludge using a novel method of electro-osmosis vacuum preloading

This case study proposed a novel electro-osmosis PRD vacuum preloading method to solve dredging sludge treatment issues: difficulty in draining from soil showing large volume, non-uniform settlement, and low strength. To verify the effectiveness of the new method, four kinds of physical model tests integrating particle image velocimetry (PIV) technique of traditional vacuum preloading (VP), prefabricated radiant drain vacuum preloading (PRD-VP), electro-osmotic vacuum preloading (EO-VP), and EO-PRD-VP methods are conducted. The water discharge, average surface settlement, pore water pressure, water content, and undrained shear strength after treatment, clogging range, relationship between clogging range and water discharge rate, and relationship between clogging range and average surface settlement are investigated. For those model tests, it is demonstrated that EO-PRD-VP method has the best advantage in volume reduction, uniform settlement, and strength improvement. Water discharge is enlarged by 13–33%. The differential settlement can reach 2.3 cm, decreased by 28–56%. The undrained shear strength can reach 12 kPa, increased by 1–2 times. In addition, the clogging range development is described, for the given water discharge rate and average surface settlement, clogging range of EO-PRD-VP method is the minimum. The empirical equations between clogging range and water discharge rate, clogging range, and average surface settlement are established to predict the clogging range, which can lay the foundation for developing the consolidation theory of EO-PRD-VP method.

An Experimental Study of the Effects of Asymmetric Pitching Motion on the Hydrodynamic Propulsion of a Flapping Fin

An Experimental Study of the Effects of Asymmetric Pitching Motion on the Hydrodynamic Propulsion of a Flapping Fin

Noise Control of Blunt Flat-Plate Using Slit and Dielectric Barrier Discharge Plasma

This paper investigates the combination of a slit at the blunt trailing edge of the flat plate and dielectric barrier discharge plasma to control the vortex shedding of the plate and its associated tonal noise. The noise and flow characteristics of the plate were measured using a far-field microphone array and the particle image velocimetry technique, respectively. The results show that the vortex shedding and the tonal noise can be significantly suppressed by the slit alone, with an average noise reduction of approximately 10 dB in the test Reynolds number. In addition, installing a plasma actuator inside the slit further suppresses the vortex shedding and reduces tonal noise. However, the additional control efficiency of the plasma decreases with increasing wind speeds, with a further 8 dB reduction at a wind speed of U∞=10  m/s (corresponding to an inducing blowing rate BR of 4.5%). However, only an additional 1.5 dB noise reduction is achieved at U∞=20  m/s (BR=2.25%). The particle image velocimetry snapshots were analyzed by proper orthogonal decomposition. The measurements clearly show the variation in vortex shedding at the trailing edge of the plate, revealing the underlying flow mechanisms that lead to the observed noise variations and frequency changes.

Experimental investigation of propagation evolution characteristics of internal solitary waves passing through downslope topography

In contrast to the extensive research on the propagation evolution of internal solitary waves (ISWs) over continental shelf topography, few investigations have been conducted on the propagation evolution of ISWs over downslope topography. In this experiment, the characteristics of the ISWs passing over a downslope topography were investigated in an immiscible two-layer fluid system to clearly capture the waveform information. The main objective of this study was to analyze the propagation evolution of ISWs with different incident amplitudes passing through a downslope topography. Using the particle image velocimetry technique, the evolutionary characteristics of ISWs (such as waveform, wave height, energy budget, and flow field) are investigated. According to the flow field analysis results, the phase velocity near the downslope topography changes with the propagation of ISWs. Moreover, the gradient distribution of velocity progressively becomes perpendicular to the right surface of the topography. Furthermore, a counterclockwise vortex gradually forms at the right upper vertex of the topography. The propagation of ISWs is influenced by varying water depth and topography. The front waveform of ISWs is significantly flat, and the back is steeper than the original back waveform. Around the tail wave, an upward convex wave packet is generated. The trends of wave energy and wave height losses are broadly consistent. Furthermore, the energy loss is related to the incident wave height with a 20% higher loss rate for large-amplitude ISWs than small-amplitude ISWs at the inflection point of the topography.

High-resolution velocity determination from particle images via neural networks with optical flow velocimetry regularization

Particle image velocimetry (PIV) and optical flow velocimetry (OFV) are important velocity measurement methods in the field of fluid dynamics. Nevertheless, the conventional cross correlation-based PIV method is beset by diminished resolution, while the OFV method exhibits computational sluggishness and susceptibility to noise. These constraints have somewhat delimited the applicability of PIV and OFV techniques. Recent attempts have introduced deep learning-based methods for analyzing PIV images, offering high-resolution velocity fields with computational efficiency, but their accuracy needs improvement. This study proposes four neural networks based on the well-established FlowNetS. They incorporate two distinct velocity constraints, namely, first-order velocity smoothing regularization and second-order grad (curl)–grad (div) regularization. In the networks, these constraints are used either independently or in combination with optical flow conservation (OFC). The performances of the networks have been assessed on six different flow configurations, and the results show that the network with the second-order regularization markedly outperforms the original network across all flows, demonstrating an enhanced capacity to capture larger-scale vortices. The network with the first-order regularization also exhibits superior performance compared to the original network except in the case of cylinder flow. Unexpectedly, the introduction of the OFC constraints results in a decline in network performance. This anomaly may stem from the network's inherent capability to capture optical flow features, rendering the OFC constraint less effective in providing guidance. In summary, this study underscores the substantial potential of neural networks incorporated with judicious physical constraints in PIV applications, enabling the determination of high-resolution, high-accuracy flow fields.